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UKMT Senior Mathematical Challenge, 2020

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The shaded area shown in the diagram consists of the interior of a circle of radius 3 together with the area between the circle and two tangents to the circle. The angle between the tangents at the point where they meet is $60°$ . What is the shaded area?

(A) $6\pi + 9\sqrt{3}$ (B) $15\sqrt{3}$ (C) $9\pi$ (D) $9\pi + 4\sqrt{3}$ (E) $6\pi + \dfrac{9\sqrt{3}}{4}$

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